A Novel Material for in Situ Construction on Mars: Experiments and Numerical Simulations

Construction and Building Materials 120 (2016) 222–231

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Construction and Building Materials

journal homepage: www.elsevier.com/locate/conbuildmat

A novel material for in situ construction on Mars: experiments and numerical simulations

a b a, Lin Wan , Roman Wendner , Gianluca Cusatis ⇑

a Department of Civil and Environmental Engineering, Northwestern University, 2145 Sheridan Rd. Evanston, IL 60208, USA b Christian Doppler Laboratory LiCRoFast, Department of Civil Engineering and Natural Hazards, University of Natural Resources and Life Sciences (BOKU) Vienna, Austria

highlights

The developed Martian Concrete is highly feasible for construction on Mars. The optimal Martian Concrete mix consists of 50% sulfur and 50% regolith. The Martian Concrete is mechanically simulated by a discrete particle model. The Martian Concrete has compressive strength of above 50 MPa.

article info abstract

Article history: A significant step in space exploration during the 21st century will be human settlement on Mars. Instead Received 14 December 2015 of transporting all the construction materials from Earth to the red planet with incredibly high cost, using Received in revised form 26 April 2016 Martian soil to construct a site on Mars is a superior choice. Knowing that Mars has long been considered Accepted 4 May 2016 a ‘‘sulfur-rich planet”, a new construction material composed of simulated Martian soil and molten sulfur is developed. In addition to the raw material availability for producing sulfur concrete and a strength reaching similar or higher levels of conventional cementitious concrete, fast curing, low temperature sus- Keywords: tainability, acid and salt environment resistance, 100% recyclability are appealing superior characteristics Martian Concrete of the developed Martian Concrete. In this study, different percentages of sulfur are investigated to obtain Sulfur concrete Waterless concrete the optimal mixing proportions. Three point bending, unconfined compression and splitting tests were Space construction conducted to determine strength development, strength variability, and failure mechanisms. The test Compression results show that the strength of Martian Concrete doubles that of sulfur concrete utilizing regular sand. Bending It is also shown that the particle size distribution plays an important role in the mixture’s final strength. Lattice Discrete Particle Model Furthermore, since Martian soil is metal rich, sulfates and, potentially, polysulfates are also formed dur- Particle size distribution ing high temperature mixing, which might contribute to the high strength. The optimal mix developed as High strength Martian Concrete has an unconfined compressive strength of above 50 MPa. The formulated Martian Concrete is simulated by the Lattice Discrete Particle Model (LDPM), which exhibits excellent ability in modeling the material response under various loading conditions. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction ancient Chinese [29]; sulfur was also used to anchor metal in stone during the 17th century [6]. Starting in the 1920s, sulfur concrete Sulfur has been used as a molten bonding agent for quite a long has been reported to be utilized as a construction material [24]. time in human history. The use of sulfur was mentioned in the lit- Various researchers and engineers studied and succeeded in erature of ancient India, Greece, China and Egypt [7]. For example, obtaining high-strength and acid-resistant sulfur concretes [1–3]. sulfur was one of the raw materials to manufacture gunpowder by In the late 1960s, Dale and Ludwig pointed out the signiﬁcance of well-graded aggregate in obtaining optimum strength [4,5]. When elemental sulfur and aggregate are hot-mixed, cast, and Corresponding author at: Department of Civil and Environmental Engineering, ⇑ Tech Building A125, Northwestern University, 2145 Sheridan Rd., Evanston, IL cooled to prepare sulfur concrete products, the sulfur binder, on 60208, USA. cooling from the liquid state, ﬁrst crystallizes as monoclinic sulfur

E-mail addresses: [email protected] (L. Wan), roman.wendner@boku. (Sb) at 238 °F (114 °C). On further cooling to below 204 °F (96 °C), ac.at (R. Wendner), [email protected] (G. Cusatis). Sb starts to transform to orthorhombic sulfur (Sa), which is the URL: http://www.cusatis.us (G. Cusatis).

http://dx.doi.org/10.1016/j.conbuildmat.2016.05.046 0950-0618/Ó 2016 Elsevier Ltd. All rights reserved. L. Wan et al. / Construction and Building Materials 120 (2016) 222–231 223 stable form of sulfur at ambient room temperatures [8]. This trans- samples failed at about 7 MPa under compression, which is about formation is rapid, generally occurring in less than 24 h and result- 1/5 of the average strength, 35 MPa, of the non-cycled samples. ing in a solid construction material. However, since Sa is much While the moon is the closest and only satellite of earth, its denser than Sb, high stress and cavities can be induced by sulfur near-vacuum environment, broad temperature range and long shrinkage. Hence, durability of unmodified sulfur concrete is a day-night rhythm, about 30 earth days, are not the most adequate problem when exposed to humid environment or after immersion for human settlement. Venus is the closest planet to Earth, how- in water. In the 1970s, researchers developed techniques to modify ever it is also the hottest planet in the solar system with an average the sulfur by reacting it with olefinic hydrocarbon polymers [9,16], surface temperature over 400 °C [45], making it uninhabitable for dicyclopentadiene (DCPD) [10,12,11,15,17], or other additives and humans. Mars, on the other hand, is not too hot nor too cold, and stabilizers [13,14,18] to improve durability of the product. Since has an atmosphere to protect humans from radiation. Its day/night then, commercial production and installation of corrosion- rhythm is very similar to that on Earth: a Mars day is about 24 h resistant sulfur concrete has been increasing, either precast or and 37 min [25]. Thus, Mars is the most habitable planet in the installed directly in industrial plants where portland cement con- solar system after Earth. In recent years, many countries, including crete materials fail from acid and salt corrosion [24]. the U.S., China, and Russia, announced to launch manned Mars For earth applications, well developed sulfur concrete features missions in the next decades. Due to the dry environment on Mars, (1) improved mechanical performance: high compressive & flexu- sulfur concrete is a superior choice for building a human village on ral strength, high durability, acid & salt water resistant, excellent the red planet. Studies of Martian meteorites suggest elevated sul- surface finish and pigmentation, superior freeze/thaw perfor- fur concentrations in the interior, and Martian surface deposits mance; (2) cost benefits: faster setting-solid within hours instead contain high levels of sulfur (SO3 up to 37 wt%, average 6 wt%), of weeks, increased tolerance to aggregate choice; and (3) environ- likely in the forms of sulfide minerals and sulfate salts [37]. Except mentally friendly profile: reduced CO2 footprint, no water require- of the easiest option of finding a sulfur mine on Mars, like the one ments, easily obtainable sulfur as a byproduct of gasoline in Sicily on Earth, elemental sulfur can be extracted from sulfides production, recyclability via re-casting, compatibility with ecosys- or sulfates through various chemical and physical processes, for tem, e.g. for marine applications. Current pre-cast sulfur concrete example, by heating up the sulfur compounds [19]. NASA has products include, but are not limited to, flagstones, umbrella advanced programs on In Situ Resources Utilization (ISRU) [30] stands, counterweights for high voltage lines, and drainage chan- for this specific purpose. Moreover, the atmospheric pressure nels [38]. (0.636 kPa) [34] as well as temperature range (635 °C) are highly For example, in January 2009, around 80 m sewage pipeline in suitable for the application of sulfur concrete. As shown in Fig. 1 the United Arab Emirates (UAE) was removed and replaced by sul- [31], the most possible construction site on Mars has environmen- fur concrete. In the same time period, a total of 215 fish reef blocks tal conditions in the Rhombic (stable) state of sulfur and is three made of sulfur concrete (2.2 tons/block) were stacked at a depth of orders of magnitude in pressure above the solid–vapor interface. 15 m, 6 km off the coast of UAE [35]. With regular concrete fish Thus, sublimation is not an issue and a relatively warm area can reefs, the growth of algae and shells takes time because concrete be selected as the construction site. Furthermore, with the temper- is alkaline. However, since sulfur concrete is practically neutral ature on Mars lower than 35 °C, the drawback of sulfur concrete in alkalinity, algae and shell growth was observed soon after melting at high temperature will not be an issue for initial con- installation. structions such as shelters and roads while certainly might be of While sulfur concrete found its way into practice as an infras- concern for long term settlements in which fire resistance would tructure material, it is also a superior choice for space construction be important. considering the very low water availability on the nearby planets and satellites [23]. After mankind stepped on the lunar surface in 1969, space agencies have been planning to go back and build a research center on the moon. Since local material is preferred to reduce expenses, starting in the early 1990s, NASA and collabora- tive researchers studied and developed lunar concrete using molten sulfur. Around the year 1993, Omar [20] made lunar concrete by mixing lunar soil simulant with different sulfur ratio ranging from 25% up to 70% and found the optimum mix with 35% sulfur to reach a compressive strength of 34 MPa. Later he added 2% of steel fibers to the mixes and increased the optimum strength to 43 MPa. However, lunar concrete has serious sublimation issues because of the near-vacuum environment on the moon. In 2008, Grugel and Toutanji [31,33,41] reported experimental results of two lunar concrete mixes: (1) 35% sulfur with 65% lunar soil simulant JSC-1, and (2) 25% sulfur and 20% silica binder mixture with 55% JSC-1. The two mixtures, similar in strength ( 35 MPa), revealed a continuous weight loss due to the sublimation of sulfur 7 when placed in a vacuum environment, 5 10À torr, at 20 °C for Â 60 days. Based on the measurements, it was predicted that sublimation of a 1 cm deep layer from the two sulfur concrete mixes would take 4.4 and 6.5 years respectively. The sublimation rate varied from rapid at the high lunar temperatures (<120 °C) to essentially nonexistent at the low lunar temperatures ( 180 °C– À 220 °C). However, the low temperature on the moon is too harsh À to maintain intact mechanical properties of sulfur concrete. After Fig. 1. Sulfur phase diagram with labeled environmental conditions on Mars and cycled 80 times between 191 °C( 312 °F) and 20 °C (68 °F), the Moon [31]. À À 224 L. Wan et al. / Construction and Building Materials 120 (2016) 222–231

Table 1 tests. Beams of dimensions 25.4 25.4 127 mm (1 1 5 in) Â Â Â Â Major element composition of Martian regolith simulant JSC Mars-1A [32]. are used for TPB tests, which are then cut to 25.4 mm (1 in) cubes Major element composition % by Wt. for compression and splitting tests.

Silicon dioxide (SiO2) 34.5–44

Titanium dioxide (TiO2) 3–4 2.1. Unconﬁned compression test

Aluminum oxide (Al2O3) 18.5–23.5 Ferric oxide (Fe2O3) 9–12 Unconfined compression tests were performed in a closed loop Iron oxide (FeO) 2.5–3.5 Magnesium oxide (MgO) 2.5–3.5 servo–hydraulic load frame with a maximum capacity of 489 kN Calcium oxide (CaO) 5–6 (110 kips). Stroke/displacement control with a loading rate of Sodium oxide (Na2O) 2–2.5 0.003 mm/s was applied. In order to ensure consistent and accu- Potassium oxide (K2O) 0.5–0.6 rate test results, a Standard Operation Procedure (SOP) for testing Manganese oxide (MnO) 0.2–0.3 was created. The test protocol was first filled with the relevant Diphosphorus pentoxide (P2O5) 0.7–0.9 details, which include Vernier Caliper measurements of each dimension (average of 2–4 measurements), the initial weight, the label of the specimen, control mode, loading rate, and start time To let the thoughts become facts, a new construction material of loading. Pictures were taken to document the initial condition using simulated Martian soil and molten sulfur is developed in this of the specimen, during test and post test states. A preload of study. Different percentages of sulfur are studied to obtain the approximately 1–5% of the expected peak-load was applied before optimal mixing proportions. Through mechanical tests, it is found the actual test commenced. that Martian Concrete has much higher strengths than sulfur con- Specimens used for unconfined compression tests were crete utilizing regular sand. Sieve analysis and chemical analysis 25.4 mm (1 in) cubes cut from the undamaged parts of provide a possible explanation for the higher strength of Martian 25.4 25.4 127 mm (1 1 5 in) beams, see Fig. 3a. The cubes Concrete: the Martian soil simulant has a better particle size distri- Â Â Â Â were cut out of the 62 mm (2.5 in) long failed half’s at the center bution, it is also rich in metal elements, which react with sulfur, between bending test support point and fracture surface. Typical forming polysulfates and possibly enhancing strengths. Mechanical cone type failure is observed under unconfined compression, as simulations of Martian Concrete are then carried out using the shown in Fig. 3b. state-of-art Lattice Discrete Particle Model with excellent simula- The studied sulfur ratio for Martian Concrete under compres- tion of Martian Concrete mechanical properties. sion ranged from 35 wt% to 60 wt%. Compressive strength versus percentage of sulfur is shown in Fig. 4 (circles), revealing an opti- 2. Experimental study of Martian Concrete mum percentage around 50% (±2.5%). Furthermore, the test results indicate that recast can further increase the strength of the mate- Sulfur concrete products are manufactured by hot-mixing sul- rial. For 50% sulfur batches, recast made compressive strength go fur and aggregate. The sulfur binder first crystalizes as monoclinic up from 48 MPa to about 58–63 MPa, which is roughly a 20–30% sulfur (Sb), and then the mixture cools down while sulfur trans- increase, see Fig. 4 labeled as ‘‘Mars1A 1 mm R.”. Furthermore, bet- forms to the stable orthorhombic polymorph (Sa), achieving a reli- ter mixing and applying pressure while placing the material in able construction material. While sulfur is commercially available, formwork facilitates material strength. In the experimental cam- Martian soil simulant JSC Mars-1A [32] was obtained in replace- paign of this study, a well distributed pressure was manually ment of Martian soil to develop a feasible Martian Concrete. Table 1 added to the mixture in the formwork, and thus the pressure lists the major element composition of the simulant. As seen, the was not quantified. Making the mixture compact facilitates forma- Martian soil simulant, resembling the actual Martian soil [22], is tion of sulfur bonds and also reduces the number and size of cav- rich with metal element oxides, especially aluminium oxide and ities of the final product. Average compressive stress–strain ferric oxide. In this study, various percentages of sulfur are mixed curves for MC with a sulfur ratio ranging from 40% to 60% are plot- with JSC Mars-1A in a heated mixer at above 120 °C. Temperature ted in Fig. 5a. Stress is calculated as P/A, where P is load and A is the measurements are performed during mixing to ensure sulfur melt- area of the cross section; strain is calculated as Dh=h, where h is the ing. Then the mixture is transferred to 25.4 25.4 127 mm height of the specimen. The stress–strain curves feature a typical Â Â (1 1 5 in) aluminum formwork when it reached flowable state almost-linear behavior up to the peak and a long stable softening Â Â or best mixing conditions. Afterwards the material was let to cool post-peak. down at room temperature, about 20 °C. Martian soil simulant While Martian Concrete has a high strength of over 50 MPa with Mars-1A of maximum 5 mm aggregate size was first used for cast- relatively high percentage of sulfur, sulfur concrete made of regu- ing, however the specimens showed many voids and uneven sur- lar sand (Sand Concrete, SC) was cast and tested as well for com- faces due to the large aggregate, see Fig. 2a. Sulfur cannot be parison. With the same dimension of 25.4 mm (1 in), SC cubes ensured to fill the large number of big voids or to surround and were cast with a sulfur ratio in the range of 15%–35%. Sand with bind all large aggregates, especially on the specimen surface. After- a maximum aggregate size of 11 mm was first utilized. Then for wards, only Mars-1A of maximum 1 mm aggregate size was uti- comparison purposes, maximum 1 mm sand, sieved from the coar- lized to achieve Martian Concrete (MC) with flat and smooth ser sand, was used as well. Following the same test procedure, SC surfaces, see Fig. 2b. Mechanical tests were conducted after 24 h, specimens were tested under unconfined compression loads. As and these included unconfined compression, notched and shown in Fig. 4, the best percentage of sulfur for SC was found to unnotched three-point-bending (TPB), and splitting (Brazilian) be about 25% for both fine (crosses in Fig. 4) and coarse (squares

Fig. 2. Martian Concrete beams utilizing Martian soil simulant with (a) maximum 5 mm aggregate, and (b) maximum 1 mm aggregate. L. Wan et al. / Construction and Building Materials 120 (2016) 222–231 225

Fig. 3. Cube specimen (a) before and (b) after unconﬁned compression test.

70 100 Mars1A 1mm 60 Mars1A 1mm R. Sand 11 mm 80 50 Sand 1 mm Sand1A 1 mm 60 40 ASTM 9.5mm ASTM 12.5mm 30 40 ASTM 19mm ASTM 25mm 20 AASHTO 4.75mm 20 Mars1A 1mm 10 Sand 11mm Fuller 0 0 0 20 40 60 80 100 0 0.2 0.4 0.6 0.8 1

Fig. 4. Compression strength variation as a function of percentage of sulfur for Fig. 6. Particle size distribution (PSD) study of Martian soil simulant and regular Martian Concrete. sand as well as ASTM and AASHTO recommended PSD for mixing sulfur concrete. in Fig. 4) mixes, having 24.5 MPa and 28.3 MPa compressive and the corresponding particle size distribution (PSD) on material strength, respectively. The results obtained on the SC mixes are strength, sieve analyses of Mars-1A (maximum 1 mm aggregate consistent with the existing literature on standard sulfur concrete size) as well as regular sand (maximum 11 mm aggregate size) [24]. When the aggregate size distribution of the fine sand was were conducted. Also included in the PSD analysis were the recom- modified based upon the particle size distribution of Mars-1A sim- mended PSDs by ASTM and AASHTO standards for mixing sulfur ulant, its SC mix’s stregnth had a 29% jump to 31.5 MPa, see Fig. 4 concrete [24]. In Fig. 6, the normalized distributions of Mars-1A, labeled as ‘‘Sand1A 1 mm” and marked with a diamond symbol. regular sand, the ASTM D 3515 and AASHTO recommended PSD This indicates and confirms the significance of the particle size dis- ranges as well as Fuller’s law with power 1/2 are plotted and com- tribution in order to obtain an optimum material strength. pared. Overall, the PSD of Mars-1A falls well in the recommended PSD range according to standards and is relatively close to Fuller’s 2.2. Particle size distribution analysis law, while the PSD of regular sand misses the recommended PSD range and also deviates from Fuller’s law. While this finding While 25% of elemental sulfur works the best for both mixes explains partly the difference in the measured strength of MC with regular sand, they also both have much lower strength com- and SC, it cannot justify the more than doubled strength of MC pared to Martian Concrete. To study the influence of aggregates compared to SC.

2 40% Sulfur 60 45% Sulfur 40% Sulfur 1.5 47.5% Sulfur 45% Sulfur 50% Sulfur ] 47.5% Sulfur 52.5% Sulfur 40 50% Sulfur 60% Sulfur 52.5% Sulfur 1 60% Sulfur 20 0.5

0 0 0.02 0.04 0.06 0.08 0 0 0.005 0.01 0.015

Fig. 5. Comparison of the response for Martian Concrete with various sulfur ratio by (a) compression and (b) 50% notched three point bending tests. 226 L. Wan et al. / Construction and Building Materials 120 (2016) 222–231

Fig. 7. Microscopy study of sulfur concrete on 1 mm scale with compositions of (a) 50% sulfur and 50% Martian soil simulant (b) 25% sulfur and 75% regular sand anda maximum particle size of 1 mm.

Fig. 8. Microscopy study of sulfur concrete on 400 lm scale with compositions of (a) 50% sulfur and 50% Martian soil simulant (b) 25% sulfur and 75% regular sand and a maximum particle size of 1 mm.

2.3. Microscopy study specimens with nominal dimensions 25.4 25.4 127 mm Â Â (1 1 5 in) were cast to perform three-point-bending (TPB) Â Â In addition to the PSD of aggregate, other factors must play a tests. The beam specimens featured a half-depth notch at midspan role concerning the final strength obtained in MC experiments. cut with a diamond coated band-saw machine. Testing notched Figs. 7 and 8 show the microscope study of Martian Concrete samples is customary in fracture mechanics to control the fracture (MC) and sulfur concrete with regular sand (SC) with optimal com- onset and to capture post-peak behavior. Dimension and weight positions. By comparing the particles of MC and SC in the measurements were recorded on specifically optimized TPB proto- mesostructure pictures, a few observations are in order. Firstly, cols. Centerline on top of specimen, and support lines at the bot- the visible average particle size of MC is much smaller than that tom were pre-marked then aligned within the servo–hydraulic of SC after hot mixing, although both mixes use aggregate with load frame, which had a capacity of 22.2 kN (5 kip). The adopted maximum particle size up to 1 mm. After casting and curing, the TPB test setup is shown in Fig. 9a. The nominal span (distance aggregate particles and their sizes can be well distinguished for between bottom supports) was 101.6 mm (4 in). An extensometer SC; on the contrary, the majority of MC particles are below 500 sensor was glued to the bottom of the specimens with the notch in microns. Secondly, the MC mix has many red areas, dark spots between its two feet. After applying a pre-load of up to 5% of the and almost no voids, while the SC mix shows distinguishably yel- expected peak, the specimens were loaded in crack mouth opening low areas of sulfur, opaque orange to dark red spots related to sand displacement (CMOD) control with a loading rate of 0.0001 mm/s, particles and a number of voids of around 200 microns. These which was increased in the post-peak section to limit the total observations, along with preliminary X-ray photoelectron spec- testing time while ensuring a fully recorded softening behavior. troscopy (XPS) tests, suggest that the metal elements in Mars-1A Typical crack propagation and fracture surface after failure are pre- react with sulfur during hot mixing, forming sulfates and polysul- sented in Fig. 9b and c. The crack starts at the notch tip and devel- fates, and altering the PSD of aggregates to lower ends, which fur- ops upward along the ligament. ther enhance the MC strength. SC does not have such phenomena Notched (50%) fracture test stress–strain curves of MC with a because silica sand does not react with sulfur at the aforemen- sulfur ratio in the range of 40%–60% are plotted in Fig. 5b. The nom- tioned casting conditions. In other words, in MC the aggregate is inal flexural stress is calculated as r 3PL=2bh2, where P is load, ¼ chemically active whereas in SC it is inert and sulfur only serves and L; b, and h are span, width, and depth of the specimen respec- as ‘‘glue” for the sand particles. The existence of sulfates and poly- tively; the nominal strain is calculated as CMOD=h. The opti- ¼ sulfates in MC are qualitatively confirmed by XPS by analyzing the mal percentage of sulfur is found to be 50% (±2.5%) which gives a chemical state of sulfur and individual metal elements within 900 nominal flexural strength of approximately 1.65 MPa, and it agrees micron-diameter areas of a thin MC sample. Definitely, further with the optimal percentage determined from unconfined com- research is needed to clearly identify the chemical products pression tests. The highest nominal flexural strength obtained is characterizing MC internal structure. 2.3 MPa reached by one of the two recast 50% sulfur batches, as shown in Fig. 10a. It must be observed that the nominal flexural 2.4. Three-point-bending fracture test strength and flexural nominal stress–strain curves are not material properties, due to the presence of the notch, and they are calcu- To complete the mechanical characterization of MC, its fractur- lated here only for comparison purposes. The typical material ing behavior is studied in this section and the next. Beam property that can be calculated from TPB test is the fracture L. Wan et al. / Construction and Building Materials 120 (2016) 222–231 227

Fig. 9. (a) Three point bending (TPB) test setup, (b) fracture surface and (c) typical crack propagation after bending test of Martian Concrete.

2.5 100 Cast Cast 2 Recast 80 Recast

1.5 60

1 40

0.5 20

0 0 40 45 50 55 60 40 45 50 55 60

Fig. 10. Best percentage of sulfur for Martian Concrete by TPB test results (a) nominal flexural strength, and (b) fracture energy. energy, defined as the energy per unit area needed to create a unit Fig. 16b, where nominal strain is calculated as vertical displace- stress-free fracture area. By adopting the work-of-fracture method ment divided by the specimen height. [21] the fracture energy is computed by dividing the area under the Modulus of rupture (MOR) tests were carried out for MC with load vs. stroke curve by the ligament area. The highest average the optimum mix, 50% sulfur and 50% Martian soil simulant. total fracture energy is as well reached by the recast Martian Con- Unnotched beams with dimensions 25.4 25.4 127 mm Â Â crete with 50% sulfur with a value of 67 J/m2, as shown in Fig. 10b. (1 1 5 in) were tested for MOR using the aforementioned Â Â When mixed with lower or higher sulfur ratio than 50%, MC has machine and setup for notched TPB but by stroke control with lower fracture energies, see Fig. 5b and Fig. 10b. Same as for com- loading rate 0.001 mm/s. The developed MC has an average MOR pressive strength, recast and applying pressure can improve the value of 7.24 MPa, see Fig. 16a. The nominal MOR stress is calcu- flexural strength thanks to more compact sulfur bonds. lated as r 3PL=2bh2, where P is load, L; b, and h are span, width, ¼ and depth of the specimen respectively; the nominal strain is cal- 2.5. Splitting and modulus of rupture tests culated as vertical displacement divided by specimen depth.

Splitting tests on 25.4 mm (1 in) cubes were performed by the 3. Lattice Discrete Particle Model simulations same load frame as for compression. Roughly 1 mm diameter bars were placed on the top and at the bottom of the specimen. A load- For design and analysis purposes it is important to formulate ing rate of 0.003 mm/s was applied until failure of the specimen at and validate a computational model for the simulation of Martian peak load. Only recast Martian Concrete with 47.5%, 50%, and 52.5% Concrete. This is pursued within the theoretical framework of the sulfur ratio were tested, and provided splitting tensile strength of Lattice Discrete Particle Model (LDPM). 3.6 MPa ± 30%, 3.9 MPa ± 28%, and 2.72 MPa ± 26% respectively. In 2011, building on previous work [26–28], Cusatis and The splitting tensile strength is calculated as r 2P=pbh, where coworkers [39,40] developed LDPM, a mesoscale discrete model ¼ P is load, b and h are the depth and height of the cube specimen that simulates the mechanical interaction of coarse aggregate respectively. In agreement with compression and TPB test results, pieces embedded in a binding matrix. The geometrical representa- splitting tests again conﬁrm that MC with 50% of sulfur have the tion of concrete mesostructure is constructed by randomly intro- highest performance. The splitting nominal stress–strain curves, ducing and distributing spherical shaped coarse aggregate pieces until failure at peak load, of the optimum MC are shown in inside the volume of interest and zero-radius aggregate pieces on 228 L. Wan et al. / Construction and Building Materials 120 (2016) 222–231 the surface. Based on the Delaunay tetrahedralization of the gener- to a given tetrahedron. Beyond the elastic limit, rbc models À ated particle centers, a three-dimensional domain tessellation cre- pore collapse as a linear evolution of stress for increasing volu- ates a system of polyhedral cells (see Fig. 11) interacting through metric strain with stiffness Hc for eV ec1 jc0ec0 : rbc rc0 À 6 ¼ ¼ þ triangular facets and a lattice system. The full description of LDPM eV ec0 Hc rDV ; Hc rDV Hc0= 1 jc2 rDV jc1 ; rc0 is the hÀ À i ð Þ ð Þ¼ ð þ hÀ iÞ geometry is reported in Cusatis. et. al. [39,40]. mesoscale compressive yield stress; rDV eD=eV and jc1; jc2 are ¼ In LDPM, rigid body kinematics is used to describe the deforma- material parameters. Compaction and rehardening occur beyond tion of the lattice particle system and the displacement jump, suC t, pore collapse ( eV P ec1). In this case one has rbc rc1 rDV exp À ¼ ð Þ at the centroid of each facet is used to deﬁne measures of strain as eV ec1 Hc rDV =rc1 rDV and rc1 rDV rc0 ec1 ec0 Hc rDV . ½ðÀ À Þ ð Þ ð Þ ð Þ¼ þð À Þ ð Þ

T T T n suC t l suC t m suC t e ; e ; e 1 N ¼ ‘ L ¼ ‘ M ¼ ‘ ð Þ Friction due to compression-shear where ‘ interparticle distance; and n; l, and m, are unit vectors For compression dominated loading conditions (eNÃ < 0), the ¼ p defining a local system of reference attached to each facet. A incremental shear stresses are computed as t_ E e_ Ã e_ Ã and M ¼ T ð M À M Þ vectorial constitutive law governing the material behavior is _ p p _ p _ tL ET e_ LÃ e_ LÃ , where e_ MÃ n@u=@tM, e_ LÃ n@u=@tL, and n is the imposed at the centroid of each facet. In the elastic regime, the ¼ ð À Þ ¼ ¼ plastic multiplier with loading–unloading conditions un_ 6 0 and normal and shear stresses are proportional to the corresponding 2 2 0 0 _ 0. The plastic potential is defined as t t t , strains: t E eÃ E e e ; t E eÃ E e e ; t E eÃ n P u M L rbs N N ¼ N N ¼ Nð N À NÞ M ¼ T M ¼ T ð M À MÞ L ¼ T L ¼ ¼ þ À ð Þ 0 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ET eL e , where EN E0;ET aE0; E0 effective normal modulus, where the nonlinear frictional law for the shear strength is assumed ð À L Þ ¼ ¼ ¼ 0 0 0 t t and a shear-normal coupling parameter; and e ; e ; e are to be rbs rs l0 l rN0 1 exp N=rN0 l N; rN0 is the ¼ N M L ¼ þð À 1Þ ½ À ð Þ À 1 mesoscale eigenstrains (if any present). For stresses and strains transitional normal stress; l0 and l are the initial and final inter- 1 beyond the elastic limit, the LDPM formulation considers the nal friction coefficients. following nonlinear mesoscale phenomena [26,27,39]: (1) fracture Each meso-level parameter in LDPM governs part of the and cohesion; (2) compaction and pore collapse; and (3) internal mechanical material behavior. The normal elastic modulus, which friction. refers to the stiffness for the normal facet behavior, E0, along with the coupling parametera, govern the LDPM response in the elastic Fracture and cohesion due to tension and tension-shear regime. Approximately, the macro scale Young’s modulus E and Poisson’s ratios m can be calculated as E E0 2 3a = 4 a and ¼ ð þ Þ ð þ Þ m 1 a = 4 a . Typical concrete Poisson’s ratio of about 0.18 For tensile loading (eNÃ > 0), the fracturing behavior is formulated ¼ð À Þ ð þ Þ is obtained by setting a = 0.25 [40]. The tensile strength, rt, and 2 2 2 through effective strain, eÃ eÃ a eÃ eÃ , and stress, ¼ N þ ð M þ L Þ characteristic length, ‘t, govern the strain softening behavior due 2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi to fracture in tension of LDPM facets [40], with the relation t t2 t t = , which define the normal and shear stresses N M L a 2 ¼ þð þ Þ Gt ‘trt =2E0, where Gt is the mesoscale fracture energy. Calibra- as tNqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffieNÃ t=eÃ ; tM aeMÃ t=eÃ ; tL aeLÃ t=eÃ . The effective stress t ¼ ¼ ð Þ ¼ ð Þ ¼ ð Þ tion of rt and ‘t is typically achieved by fitting experimental data, is incrementally elastic (t_ E e_) and must satisfy the inequality ¼ 0 e.g. the nominal stress–strain curves of TPB tests. The yielding 0 6 t 6 rbt e; x where rbt r0 x exp H0 x e e0 x =r0 x ; ð Þ ¼ ð Þ ½À ð Þh À ð Þi ð Þ compressive stress, rc0, defines the behavior of the facet normal 2 2 x max x;0 , and tan x eÃ =paeÃ = tNpa=tT , and eÃ eÃ eÃ . component under compression. The softenig exponent, nt, governs h i¼ f g ð Þ¼ N T T ¼ M þ L qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffint the interaction between shear and tensile behavior during soften- The post peak softening modulusffiffiffi is definedffiffiffi as H0 x Ht 2x=p , ð Þ¼ ð Þ ing at the facet level and it governs the macroscopic compressive where Ht is the softening modulus in pure tension (x p=2). ¼ LDPM provides a smooth transition between pure tension and pure behavior at high confinement. One obtains more ductile behavior n shear (x 0) with parabolic variation for strength given by in both compression and tension by increasing t, however the ¼ increase is more pronounced in compression than in tension. The 2 2 2 2 2 r0 x rtr sin x sin x 4a cos x =rst = 2a cos x , initial internal friction, , mainly govern the mechanical response ð Þ¼ st À ð Þþ ð Þþ ð Þ ½ ð Þ l0 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi in compression at low confinement and have no influence on ten- where rst rs=rt is the ratio of shear strength to tensile strength. ¼ sile behavior. Descriptions of effects and functions of other LDPM mesoscale parameters and further discussions can be found in Compaction and pore collapse from compression Cusatis et. al. [40] and Wan et. al. [48]. LDPM has been utilized successfully to simulate cementitious Normal stresses for compressive loading (e < 0) must satisfy NÃ concrete behavior under various loading conditions [39,40]. Fur- the inequality rbc eD; eV 6 tN 6 0, where rbc is a strain- À ð Þ thermore, the framework has been extended to properly account dependent boundary depending on the volumetric strain, e , and V for fiber reinforcement [42,43] and has the ability to simulate the the deviatoric strain, e e e . The volumetric strain is com- D ¼ N À V mechanical behavior of ultra high performance concrete (UHPC) puted by the volume variation of the Delaunay tetrahedra as [44,46,48] and long term behavior of concrete with fastening appli- eV DV=3V and is assumed to be the same for all facets belonging ¼ 0 cations [47]. Although Martian Concrete has sulfur bonds instead of calcium- silicate-hydrate gels, it shares with cementitious concrete the heterogeneous internal structure, which is the basis of the LDPM formulation. Thus, LDPM is adopted to simulate the mechanical behavior of the Martian Concrete. The numerical simulations presented in this paper were performed with the software MARS, a multi-purpose computational code, which implements LDPM, for the explicit dynamic simulation of structural performance [36]. As aforementioned, the particle size of the aggregates in MC is shifted to lower ends after casting, however, the exact distribution cannot be obtained and simulating the smallest particles would Fig. 11. One LDPM Cell around an aggregate piece. result in significantly high computation cost. Thus, the discrete L. Wan et al. / Construction and Building Materials 120 (2016) 222–231 229

Table 2 LDPM parameters had been calibrated and determined, predictive Parameters for Martian Concrete LDPM simulations. simulations for unnotched TPB tests and splitting tests were car- Normal modulus [GPa] 10 ried out and compared to experimental data as validation. Densification ratio [–] 1 The LDPM simulation setup, typical failure type and crack prop- Tensile strength [–] [MPa] 3.7 agation of notched TPB, unconfined compression, splitting, and Yielding compressive Stress [MPa] 300 unnotched TPB tests are shown in Fig. 12–14 respectively. Note Shear Strength Ratio [–] 4 Tensile characteristic length [mm] 55 that in the notched and unnotched TPB simulation setup (Fig. 12 Softening exponent [–] 0.2 and 14), the specimen is composed of lattice discrete particles at Initial hardening modulus ratio [–] 0.12 the center and classical elastic finite elements on the two sides, Transitional strain ratio [–] 4 where only elastic deformation is expected to occur, in order to Initial friction [–] 0.1 save computational time. In the unconfined compression test simulation, high friction parameters for typical concrete-steel slippage interaction [40] are utilized: l 0:13, l 0:015, and s ¼ d ¼ s 1:3 mm, to simulate friction between the specimen ends and 0 ¼ particles are generated randomly with aggregate pieces of 0.5– the steel loading platens, assuming a slippage-dependent friction 1 mm following Fuller’s law with exponent 1/2 for each type of coefficient formulated as l s l l l s0= s0 s . The fitted ð Þ¼ d þð s À dÞ ð þ Þ specimen. The utilized mesoscale parameters for MC with the best stress–strain curves can be found in Fig. 15 and 16. Fig. 15a shows sulfur ratio (50%) are listed in Table 2. The TPB experimental data the nominal stress–strain curves for 50% notched TPB tests and the 2 was primarily utilized to calibrate the LDPM parameters governing material has total fracture energy, GF , of 67.0 J/m . The mesoscale elastic as well as fracture behavior, which include normal modulus, initial fracture energy calculated from LDPM parameters, 2 2 tensile strength, shear strength ratio, tensile characteristic length, Gt ‘tr =2E0 = 37.6 J/m , is approximately half of GF . This is due ¼ t and softening exponent. Note that the normal modulus is cali- to the fact that even under macroscopic mode I fracture the mesos- brated by the TPB test data because the nominal strain (CMOD/h) cale response is characterized by both shear and tension. Fig. 15b is directly measured on the specimens, while the deformation presents the experimental and simulated stress–strain curves of measurements of all other tests include the machine compliance. unconfined compression test. Young’s modulus E is back calculated

Compression experimental data was then used to calibrate the utilising the aforementioned equation E E0 2 3a = 4 a and ¼ ð þ Þ ð þ Þ shear strength, the softening exponent and the initial internal fric- has an average value of 6.5 GPa. This value is then used to remove tion. The other parameters’ values, relevant to confined compres- the machine compliance in experimental compression test data. sive behavior, are determined based on calibrated sets for typical Brittle failure is observed both in experiments and simulations cementitious concrete materials available in the literature [40,48] for unnotched TPB and splitting tests, as shown in Fig. 16a and b and are assumed to work also for Martian Concrete in absence of respectively. The compliance in splitting and unnotched TPB specific experimental data. The adopted values are densification experimental data is removed according to calibrated simulations. ratio = 1, asymptotic friction = 0, transitional stress = 300 MPa, vol- As pure predictions, the simulation peaks highly agree with the umetric deviatoric coupling coefficient = 0, deviatoric strain average strengths of the experiments. This indicates the superior threshold ratio = 1, and deviatoric damage parameter = 5. After all ability of LDPM to simulate and predict the mechanical behavior

Fig. 12. LDPM simulation of notched TPB test setup and zoomed-in view of crack propagation.

Fig. 13. LDPM simulation of typical crack propagation in (a) unconﬁned compression test and (b) splitting (Brazilian) test. 230 L. Wan et al. / Construction and Building Materials 120 (2016) 222–231

Fig. 14. LDPM simulation of unnotched TPB test setup and typical crack propagation.

(b) 2 EXP 60 EXP AVE SIM 1.5

40 1

EXP EXP Ave 20 0.5 SIM

0 0 0 0.005 0.01 0.015 0 0.02 0.04 0.06 0.08

Fig. 15. Experimental results and LDPM simulations for calibration and validation: (a) 50% notched three-point-bending tests (b) unconﬁned compression tests.

10 6

8 4 6

4 2 2

0 0 0 0.005 0.01 0.015 0 0.005 0.01 0.015 0.02 0.025

Fig. 16. Experimental results and LDPM simulations for validation: (a) unnotched three-point-bending tests (b) splitting tests. of not only cement based concrete but also the novel waterless The optimum particle size distribution (PSD) of Martian Martian Concrete materials. regolith simulant is found to play a role in achieving high strength MC compared to sulfur concrete with regular 4. Summary and conclusions sand. The rich metal elements in Martian soil simulant are found to be In conclusion, the developed sulfur based Martian Concrete is reactive with sulfur during hot mixing, possibly forming sul- feasible for construction on Mars for its easy handling, fast curing, fates and polysulfates, which further increases the MC strength. high strength, recyclability, and adaptability in dry and cold envi- Simultaneously, the particle size distribution of aggregate is ronments. Sulfur is abundant on Martian surface and Martian rego- shifted to lower ends, resulting in less voids and higher perfor- lith simulant is found to have well graded particle size distribution mance of the final mix. to ensure high strength mix. Both the atmospheric pressure and With the advantage of recyclability, recast of MC can further temperature range on Mars are adequate for hosting sulfur con- increase the material’s overall performance. crete structures. Based upon the experimental and numerical Applying pressure during casting can also increase the final results presented in this paper, the following conclusions can be strength of MC. Sulfur shrinks when it is cooling down. By drawn: reducing the mixture’s volume during casting, the number and size of cavities of the final product are decreased. The best mix for producing Martian Concrete (MC) is 50% sulfur Although developed for conventional cementitious concrete, and 50% Martian soil simulant with maximum aggregate size of the Lattice Discrete Particle Model (LDPM) shows also excellent 1 mm. The developed MC can reach compressive strength ability in simulating the mechanical behavior of MC under var- higher than 50 MPa. ious loading conditions. L. Wan et al. / Construction and Building Materials 120 (2016) 222–231 231

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